A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any element a ∈ R. We consider left APP-property of the skew formal power series ring R[[x;α]] where α is a ring automorphism of R. It is shown that if R is a ring satisfying descending chain condition on right annihilators then R[[x;α]] is left APP if and only if for any sequence (b0, b1, ....

In this paper we will investigate the interactions between the zero divisor graph, the annihilator class graph, and the associate class graph of commutative rings. Acknowledgements: We would like to thank the Center for Applied Mathematics at the University of St. Thomas for funding our research. We would also like to thank Dr. Michael Axtell for his help and guidance, as well as Darrin Weber f...

The di erential equation dX dt X k X where k is a Toeplitz annihilator has been suggested as a means to solve the inverse Toeplitz eigenvalue problem Starting with the diagonal matrix whose entries are the same as the given eigenvalues the solution ow has been observed numerically to always converge a symmetric Toeplitz matrix as t This paper is an attempt to understand the dynamics involved in...

Understanding the temperature dependency of triplet-triplet annihilation upconversion (TTA-UC) is important for optimizing biological applications of upconversion. Here the temperature dependency of red-to-blue TTA-UC is reported in a variety of neutral PEGylated phospholipid liposomes. In these systems a delicate balance between lateral diffusion rate of the dyes, annihilator aggregation, and ...

We provide a micro-local necessary condition for distinction of admissible representations real reductive groups in the context spherical pairs. Let $\bf G$ be complex algebraic group, and H\subset subgroup. $\mathfrak{g},\mathfrak{h}$ denote Lie algebras H$, let $\mathfrak{h}^{\bot}$ annihilator $\mathfrak{h}$ $\mathfrak{g}^*$. A $\mathfrak{g}$-module is called $\mathfrak{h}$-distinguished if ...

Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely strongly coprimal and super coprimal modules. Denote by ZR(M) the set of all zero-divisors of R on M . M is said to be strongly coprimal (resp. super coprimal) if for arbitrary a, b ∈ ZR(M) (resp. every finite subset F of ZR(M)) the annihilator of {a, b} (resp. F ) in M is non-zero. In this paper w...